looking for a way to add note or comment to the Change Case Owner. My plan is that comment will be added to the notification email that the new owner received.
Do you know if this possible with enterprise edition
No, it's not possible to change that page.
pepefloyd is correct, you can't edit it...however you can mimic this in visualforce and an apex controller. Create a page to display and function similar to the change owner page. Create a link or button on standard layout to "Change Owner" and push that to the page. In apex you can perform the update to the owner.